Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 3x = 25

Answer 1

we are given

$x^2+3x=25$

We can complete square

we can write it as

$x^2+2*\frac{3}{2}*x=25$

now, we can add both sides (3/2)^2

$x^2+2*\frac{3}{2}*x+(\frac{3}{2})^2=25+(\frac{3}{2})^2$

now, we can use formula

$a^2+2*a*b+b^2=(a+b)^2$

we can write it as

$(x+\frac{3}{2})^2=25+(\frac{3}{2})^2$

$(x+\frac{3}{2})^2=25+\frac{9}{4}$

$(x+\frac{3}{2})^2=\frac{109}{4}$

now, we can take sqrt both sides

$\sqrt{(x+\frac{3}{2})^2}=\sqrt{\frac{109}{4} }$

we will get as

first solution:

$x+\frac{3}{2}=\frac{\sqrt{109}}{2}$

$x=-\frac{3}{2}+\frac{\sqrt{109}}{2}$

$x=3.72$

Second solution:

$x+\frac{3}{2}=-\frac{\sqrt{109}}{2}$

$x=-\frac{3}{2}-\frac{\sqrt{109}}{2}$

$x=-6.72$

so, solutions are

$x=-6.72$

$x=3.72$................Answer